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The Schwartz Alternating Algorithm for Solving 3D Exterior Helmholtz Problems

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  • Qing Chen
  • Baoqing Liu
  • Qikui Du

Abstract

Based on the natural boundary reduction, an overlapping domain decomposition method is discussed for solving exterior Helmholtz problem over a three-dimensional (3D) domain. By introducing two different artificial boundaries, the original unbounded domain is divided into a bounded subdomain and a typical unbounded region, and a Schwartz alternating method is presented. The finite element method and natural boundary element method are alternately applied to solve the problems in the bounded subdomain and the typical unbounded subdomain. Moreover, the convergence of the Schwartz alternating algorithm is studied. Finally, some numerical experiments are presented to show the performance of this method.

Suggested Citation

  • Qing Chen & Baoqing Liu & Qikui Du, 2018. "The Schwartz Alternating Algorithm for Solving 3D Exterior Helmholtz Problems," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-9, May.
    • Handle: RePEc:hin:jnlmpe:6029484
    DOI: 10.1155/2018/6029484
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